#include "brperm.h"
#include <iostream>
#include <vector>
#include <string>
#include <map>
#include <set>
#include <cmath>
#include <fstream>
#include <climits>
#include <queue>
#include <algorithm>
#include <stdint.h>
#include <stack>
#include <iomanip>
#include <unordered_set>
#include <unordered_map>
#include <cstring> // Для memset
using namespace std;
int n;
const long long MOD = 1e9 + 9;
long long p[530005], invp[530005];
long long put(long long a, long long exp)
{
if (exp == 0)
return 1;
if (exp % 2 == 0)
return put(a * a % MOD, exp / 2);
else
return put(a * a % MOD, exp / 2) * a % MOD;
}
int rev(int x, int k)
{
int aux = 0;
for (int i = 0; i < k; i++)
if (((1 << i) & x))
aux += (1 << (k - i - 1));
return aux;
}
long long hsh[500005][19];
long long normal[500005][19];
long long sump[500005];
void init(int copn, const char s[])
{
n = copn;
p[0] = 1;
p[1] = 31;
for (int i = 2; i <= (1 << 19); i++)
p[i] = (p[i - 1] * p[1]) % MOD;
for (int i = 0; i <= (1 << 19); i++)
invp[i] = put(p[i], MOD - 2);
for (int i = 0; i < n; i++)
{
hsh[i][0] = normal[i][0] = s[i];
}
for (int k = 1; k < 19; k++)
{
for (int i = 0; i + (1 << k) - 1 < n; i++)
{
hsh[i][k] = (hsh[i][k - 1] + hsh[i + (1 << (k - 1))][k - 1] * p[(1 << (18 - k))]) % MOD;
//for(int j=0;j<(1<<k);j++) normal[i][k] = (normal[i][k] + s[i+j]*p[j*(1<<(18-k))])%MOD;
}
long long pref = 0;
long long prod = 1;
for (int i = 0; i < n; i++)
{
pref = (pref + 1LL * s[i] * prod) % MOD;
sump[i] = pref;
prod = prod * p[(1 << (18 - k))] % MOD;
}
prod = 1;
for (int i = 0; i + (1 << k) - 1 < n; i++)
{
normal[i][k] = sump[i + (1 << k) - 1];
if (i > 0) normal[i][k] = (normal[i][k] + MOD - sump[i - 1]) % MOD;
normal[i][k] = normal[i][k] * prod % MOD;
prod = prod * invp[(1 << (18 - k))] % MOD;
}
}
}
int query(int i, int k)
{
if (i + (1 << k) - 1 >= n)
return 0;
return hsh[i][k] == normal[i][k];
}
